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A352421 Number of tilings of a 5 X n rectangle using n pentominoes of shapes U, Y, Z.

%I A352421 #15 Apr 20 2023 13:40:02
%S A352421 1,0,0,0,0,4,6,8,6,8,54,112,182,232,404,930,2054,3880,6304,10696,
%T A352421 20696,42396,81554,146240,259534,480084,924860,1768856,3284468,
%U A352421 5992798,11044774,20756310,39209398,73369392,135855648,251495794,468915328,878762056,1644145874
%N A352421 Number of tilings of a 5 X n rectangle using n pentominoes of shapes U, Y, Z.
%H A352421 Alois P. Heinz, <a href="/A352421/b352421.txt">Table of n, a(n) for n = 0..3699</a>
%H A352421 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A352421 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 3, 8, 8, 12, 4, 2, 11, 10, 5, -1, -29, -90, -65, -20, 39, -13, -73, -71, -110, -128, -67, 44, 82, 0, -53, 67, 70, 61, -79, -96, -3, 79, 84, 64, 30, -42, -29, -44, 24, 0, 0, 2).
%F A352421 G.f.: (16*x^42 -16*x^41 +3*x^40 -20*x^39 -28*x^38 +28*x^37 -2*x^36 +31*x^35 +15*x^34 -38*x^33 -29*x^32 +9*x^31 +20*x^30 +69*x^29 +3*x^28 -10*x^27 +10*x^26 +2*x^25 +31*x^24 -10*x^23 -20*x^22 -41*x^21 -37*x^20 -25*x^19 +7*x^18 +8*x^17 -3*x^16 -28*x^15 -31*x^14 -9*x^13 +x^12 +2*x^11 +7*x^10 +6*x^9 -2*x^8 +4*x^7 +2*x^6 +4*x^5 +3*x^4 -1) / (2*x^45 +24*x^42 -44*x^41 -29*x^40 -42*x^39 +30*x^38 +64*x^37 +84*x^36 +79*x^35 -3*x^34 -96*x^33 -79*x^32 +61*x^31 +70*x^30 +67*x^29 -53*x^28 +82*x^26 +44*x^25 -67*x^24 -128*x^23 -110*x^22 -71*x^21 -73*x^20 -13*x^19 +39*x^18 -20*x^17 -65*x^16 -90*x^15 -29*x^14 -x^13 +5*x^12 +10*x^11 +11*x^10 +2*x^9 +4*x^8 +12*x^7 +8*x^6 +8*x^5 +3*x^4 -1).
%e A352421 a(7) = 8:
%e A352421   ._____________.     ._____________.     ._____________.
%e A352421   |_. .___| | ._|     |_. .___| ._| |     | |_. .___| ._|
%e A352421   | |_| .___| | |     | |_|_. | |_. |     | ._|_| ._| | |
%e A352421   | ._|_| |___| |     | |_. | |___| |     | | ._| |___| |
%e A352421   | | .___| |_. | (4) | ._| |___| |_| (2) |_| |___| |_. | (2)
%e A352421   |_|_|_______|_|     |_|___|_______|     |___|_______|_|      .
%e A352421 .
%Y A352421 Cf. A174249, A343529, A349187.
%K A352421 nonn,easy
%O A352421 0,6
%A A352421 _Alois P. Heinz_, Apr 25 2022